Answer:
Tunnel A: Circle
Tunnel B: Parabola
Max height of A: 12 ft
Max height of B: 16 ft
The truck can only pass through tunnel B.
Step-by-step explanation:
Since we do not know what x and y represent, we assume that is the height of the tunnel and x is the width.
Part A:
Let us convert our equation into the standard form.
The equation for tunnel A is
which we rewrite as
Now we complete the square for variable x. What should we add to x^2 + 28x to make it a complete square?
After some thinking, we realise that we do x^2 + 28x + 14^2 then we have (x + 14)^2 .
Therefore, we add 14^2 to both sides of our equation to get:
this equation we recognise as that of a circle! Therefore, the conic section for tunnel A is a circle.
Part B:
Let us now turn to tunnel B and write its equation:
The first thing to note is that the above equation is linear in y; therefore, we can rearrange the equation to write it as
Now we have to complete the square on the right-hand side.
subtracting 256 from both sides gives
which is the standard equation for a parabola!
Hence, the conic section for tunnel B is that of a parabola.